Understanding the three-dimensional primary circulation of land-falling tropical cyclones (TCs) from single ground-based Doppler radar data has proved difficult despite numerous prior art approaches. A TC is typically described as a large cyclonic rotating body of winds characterized by a calm region near its circulation center. The intensity of a TC is usually classified by its surface maximum wind and/or minimum central pressure. Due to the practical limitations of dual-Doppler radar observations, prior art approaches have focused mainly on single-Doppler radar observations. One such approach is the so-called ground-based velocity track display (GBVTD) algorithm that attempts to estimate the primary circulation of atmospheric vortices, such as tropical cyclones and tornadoes. Although the GBVTD algorithm has greatly enhanced the estimation of the primary circulation of atmospheric vortices, the GBVTD algorithm has limitations in at least the following four areas: 1) distortion in the retrieved asymmetric wind fields, 2) a limited analysis domain, 3) the inability to resolve the cross-beam component of the mean wind, and 4) the inability to separate the asymmetric tangential and radial winds.
The present application overcomes some of these drawbacks and presents a new algorithm, which substantially eliminates the first two limitations inherent in the GBVTD technique and demonstrates the possibility of subjectively estimating the mean wind vector when its signature is visible beyond the influence of the vortex circulation.
According to an embodiment of the invention, the algorithm used by the present invention fits the atmospheric vortex circulation to a scaled Doppler velocity, VdD/RT, in a linear azimuth angle (θ′), rather than the Doppler velocity Vd in a nonlinear angle (ψ), which is used in GBVTD, where Vd is the Doppler velocity, D is the radial distance between the radar and the pulse volume, and RT is the distance from the radar to the estimated vortex center. Key vortex kinematic structures (e.g., mean wind, axisymmetric tangential wind, etc.) in the VdD/RT space simplify the interpretation of the radar signature and substantially eliminate the geometric distortion inherent in the Vd display used in the prior art. This is a significant improvement in diagnosing vortex structures in both operations and research. The advantages of using VdD/RT are illustrated using analytical atmospheric vortices, and the properties are compared with GBVTD. The characteristics of the VdD/RT display of Typhoon Gladys (1994) were approximated by a constant mean wind plus an axisymmetric vortex to illustrate the usefulness of the present art.
Atmospheric vortices such as tropical cyclones and tornadoes possess a dipole Doppler velocity pattern when observed by a ground-based Doppler radar scanning in a plan-position indicator (PPI) mode. The shape of the dipole Doppler velocity pattern of an axisymmetric vortex is a function of the distance between the “vortex circulation center” (hereafter, the center) and the radar, the core diameter, and the ratio of peak tangential to peak radial wind. The dipole rotates clockwise (counterclockwise) when the radial wind is inflow (outflow). When an axisymmetric vortex is located at infinite distance from the radar, its center can be determined as the midpoint of the line segment connecting the two peak dipole velocities. As the vortex approaches the radar, the peak velocities of the dipole move toward the radar faster than the center. Hence, the dipole pattern is distorted and the center does not fall on the line segment connecting the two peak velocities of the dipole, which increases the complexity of accurately identifying the center in operational setting.
Based on the rotational characteristics of a vortex, a prior art, single-Doppler wind retrieval methodology, called the ground-based velocity track display (GBVTD), to retrieve and display the primary kinematic structures of atmospheric vortices has been developed. FIG. 1 shows the symbols and geometry of the GBVTD technique, which is also utilized according to the present invention. The symbols in FIG. 1 are defined as follows:
O:the location of the ground-based Doppler radarT:the center of the TCR:the radial distance from the TC center to the ring at a constantaltitude where the analysis is performedE:the intersection of a radar beam and a constant radius ringA, C:the intersections of a radar beam and a ring of radius RB, H:the intersections of radar beams tangent to the ring of radius Rwhere OB ⊥ TB and OH ⊥ THF, G:FG passes through T and is perpendicular to OTD:the radial distance between the radar and a pulse volumeRT:the radial distance between the radar and the storm centerθD:the mathematical angle of the radar beam measuredcounterclockwise from the eastφ:the elevation angle of the radar beamVd:the Doppler velocityVT:the tangential velocity of the TC, positive counterclockwise(clockwise) in the Northern (Southern) HemisphereVR:the radial velocity of the TC, positive outward from the TC centerVM:the magnitude of the mean wind flowθM:the direction of the mean wind flowα:the angle subtended by OE and OT (∠TOE)αmax:the maximum α at a given radius (∠TOB)ψ:∠OET; when ψ = 0 (A) and π (C), the radar beam is parallel toradius TE; when ψ = π/2 (B) and 3π/2 (D), the radar beam isnormal to radius TEθT:the mathematical angle for TC center viewing from the radar
Using a cylindrical coordinate system with the center as the origin, the GBVTD technique performs a Fourier decomposition of the Doppler velocity Vd around each circle of radius R, and then estimates the three-dimensional (3D) tangential and radial circulations that cannot be deduced by existing single-Doppler wind retrieval methods. Plausible axisymmetric 3D kinematic and dynamic quantities, such as the angular momentum, vertical vorticity, and perturbation pressure, can also be computed from the GBVTD-retrieved axisymmetric tangential and radial winds.
A few of the limitations of the GBVTD technique are as follows: 1) distortion in the retrieved asymmetric wind fields, 2) a limited analysis domain, 3) an inability to resolve the cross-beam component of the mean wind, and 4) an inability to separate the asymmetric tangential and radial winds. The first three limitations are caused by the sampling geometry, while the last is due to the intrinsic closure assumptions of the GBVTD technique. Hence, the GBVTD-derived vortex circulation is a proxy of the “true” circulation and may inherit large uncertainties resulting from the above limitations in certain situations.
The present application provides a generalized velocity track display (GVTD) technique and its applications to atmospheric vortices. The technique of the present invention extends the foundation of GBVTD already established in an attempt to address the first three aforementioned limitations inherent in the GBVTD technique. Starting from the same radar observations, the technique used by present invention introduces a new variable VdD/RT, which is the scaled Doppler velocity, by multiplying the radial distance between the radar and a pulse volume (D) by the measured Doppler velocity Vd, and then dividing by the distance between the radar and the estimated vortex center (RT). Key vortex kinematic structures displayed in the VdD/RT space simplify the interpretation of the radar signature and eliminate the geometric distortion inherited in the Vd space. It will be shown that the present invention expands VdD/RT into Fourier coefficients in a linear coordinate (θ′) rather than expanding Vd in a nonlinear coordinate (ψ′) in GBVTD. This results in a slightly complicated but mathematically exact representation, eliminating the required approximation of cos α in GBVTD. The present invention is able to retrieve asymmetric vortex structures without distortion when the center is known accurately.